We introduce and study some mixed product Poisson structures on product
manifolds associated to Poisson Lie groups and Lie bialgebras. For
quasitriangular Lie bialgebras, our construction is equivalent to that of
fusion products of quasi-Poisson G-manifolds introduced by Alekseev, Kosmann-
Schwarzbach, and Meinrenken. Our primary examples include four series of
holomorphic Poisson structures on products of flag varieties and related spaces
of complex semi-simple Lie groups.Comment: 37 pages, submitted to IMR
